An experimenter adds 640 J of heat to 1.75 mol of an ideal gas to heat it from 1
ID: 1529628 • Letter: A
Question
An experimenter adds 640 J of heat to 1.75 mol of an ideal gas to heat it from 10.0C to 21 C at constant pressure. The gas does 160 J of work during the expansion. Part B Calculate for the gas. In an experiment to simulate conditions within an automobile engine, 0.160 mol of air at a temperature of 800 K and a pressure of 2.70×106 Pa is contained in a cylinder of volume 390 cm3 . Then 680 J of heat is transferred to the cylinder. Part A If the volume of the cylinder is constant while the heat is added, what is the final temperature of the air? Assume that the air is essentially nitrogen gas. Part B If instead the volume of the cylinder is allowed to increase while the pressure remains constant, find the final temperature of the air.
Explanation / Answer
Let Q = + 640J ( heat added to cylinder) and Work = + 160 J ( work done by system)
number of mole , n = 1.75 mol.
temperature increase ( T2 - T1 ) = 110 C
according to first law of thermodynamics
dQ = dU + dW ........... (1)
+640 = dU +160
so increase in internal energy; U = 480 J
Cp = Q / (n * (T2 - T1 ) = 33.246 J
Cv = U / ( n* (T2 - T1 ) = 24.935 J
so ( PART B ) --------Y = (Cp / Cv ) = 1.33
For the automobile engine :
n= 0.160 mol of air. = 0.160 mol of nitrogen.
T = 800 K
P = 2.70 * 106 Pa and V = 390 cm3 = 390 * 10-6 m3
heat transfered Q = +680 J ( added to the system)
if volume of the system is constant then work done will be zero.
so from equation 1.
Q = U = m Cv ( T2 - T1 ) = n* molecular mass of nitrogen * (Cv of nitrogen = 0.743 ) * ( T2 - 800)
so (Part A). T2 = 1004.287 K = final temperature.
(Part B). If the pressure of the cylinder remain constant.
Q = n* molecular mass of nitrogen * Cp * ( T2 - T1 ); where Cp of the nitrogen = 1.04
so final temperature in this case T2 = 945.948 K
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